find all unique combinations of n numbers between 1 and k

Question

I want a list of all possible sets of five (or n) numbers between 1 and 63 (or more generalizably 1 and k)

If computing time wasn't an issue, I could do something like

 #Get all combenations of numbers between 1 and 63
 indexCombinations <- expand.grid(1:63, 1:63, 1:63, 1:63, 1:63)

 #Throw out the rows that have more than one of the same number in them
 allDifferent <- apply(indexCombinations, 1, function(x){
      length(x) == length(unique(x))
 } # function
 ) # apply

 indexCombinationsValid <- indexCombinations[allDifferent,]

 # And then just take the unique values
 indexCombinationsValidUnique <- unique(indexCombinationsValid)

The finding of unique values, I am concerned, is going to be prohibitively slow. Furthermore, I end up having to make a bunch of rows in the first place I never use. I was wondering if anyone has a more elegant and efficient way of getting a data frame or matrix of unique combinations of each of five numbers (or n numbers) between one and some some range of values.

Answer 1

感谢@SymbolixAU提供一个非常优雅的解决方案，我将其在此处重新发布作为答案：

 n <- 1:63; x <- combn(n, m = 5)